210hwremarks - Comments on Homeworks 1 and 2 Homework 1,...

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Comments on Homeworks 1 and 2 Homework 1, Question 4. I wasn’t as explicit as I could have been. Technically, you could just write x (if x is real, then e x is positive) x (if x is an integer, then x can’t be both even and odd) x (if x is a prime number, there is another prime number that’s bigger) However, the sentences have more structure than that. What I had in mind was to translate further into symbols. For instance, x ± ( x is real) ( e x is positive) ² x ± ( x is an integer) → ¬ ³ ( x is even) ( x is odd) ´ ² x ± ( x is prime) → ∃ y ³ ( y is prime) ( y is greater than x ) ´ ² You can translate even further into symbols than that. For instance, you could make up symbols for predicates, such as R ( x ) = “ x is real” (we could also write “ x R ”) P ( x ) = “ x is positive” (we could also write “ x > 0”) I ( x ) = “ x is an integer” (we could also write “ x Z ”) E ( x ) = “ x is even” O ( x ) = “ x is odd” Q ( x ) = “ x
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210hwremarks - Comments on Homeworks 1 and 2 Homework 1,...

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